scholarly journals Correction: “Delta-shocks as limits of vanishing viscosity for multidimensional zero-pressure gas dynamics” [Quart. Appl. Math. 59 (2001), no. 2, 315–342; MR1827367 (2002b:76088)] by J. Li and H. Yang

2002 ◽  
Vol 60 (1) ◽  
pp. 200
Author(s):  
J. Li ◽  
H. Yang
Keyword(s):  
Gas Dynamics ◽  
Vanishing Viscosity ◽  
Delta Shocks ◽  
Appl Math

The global Hölder-continuous solution of isentropic gas dynamics

1993 ◽  
Vol 123 (2) ◽  
pp. 231-238 ◽  
Author(s):  
Yun-Guang Lu
Keyword(s):  
Cauchy Problem ◽  
Gas Dynamics ◽  
Continuous Solution ◽  
Hölder Continuous ◽  
Vanishing Viscosity ◽  
Equations Of Gas Dynamics ◽  
The Cauchy Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

SynopsisThis paper considers the Cauchy problem for the isentropic equations of gas dynamics in Euler coordinates ρt + (ρu)x = 0, (ρu)t + (ρu)2 + P(ρ))x=0 and gives the Hölder-continuous solution by applying the method of vanishing viscosity.

Vanishing viscosity for non-isentropic gas dynamics with interacting shocks

2016 ◽  
Vol 36 (6) ◽  
pp. 1699-1720 ◽  
Author(s):  
Xiaoding SHI ◽  
Yan YONG ◽  
Yinglong ZHANG
Keyword(s):  
Gas Dynamics ◽  
Vanishing Viscosity ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

scholarly journals Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations

2018 ◽  
Vol 15 (04) ◽  
pp. 721-730 ◽  
Author(s):  
Christian Klingenberg ◽  
Simon Markfelder
Keyword(s):  
Initial Data ◽  
Euler Equations ◽  
Weak Solutions ◽  
Gas Dynamics ◽  
Energy Inequality ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
Energy Equality ◽  
Compressible Euler ◽  
Appl Math

We consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this paper, we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper, we will also show that there even exist Lipschitz initial data with the same property.

Supernovae and interstellar gas dynamics

1967 ◽  
Vol 31 ◽  
pp. 117-119
Author(s):  
F. D. Kahn ◽  
L. Woltjer
Keyword(s):  
Lower Limit ◽  
High Velocity ◽  
Gas Dynamics ◽  
Interstellar Cloud ◽  
Interstellar Gas ◽  
Random Motions ◽  
Relativistic Particles

The efficiency of the transfer of energy from supernovae into interstellar cloud motions is investigated. A lower limit of about 0·002 is obtained, but values near 0·01 are more likely. Taking all uncertainties in the theory and observations into account, the energy per supernova, in the form of relativistic particles or high-velocity matter, needed to maintain the random motions in the interstellar gas is estimated as 1051·4±1ergs.

Sign in / Sign up

Export Citation Format

Share Document